Deformation Modeling of a Flexible Instrument Using a Bézier Curve

2020 ◽  
Author(s):  
Gudala Rajesh ◽  
Jitendra P. Khatait
Keyword(s):  
Strain Energy ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Body ◽  
Geometric Constraints ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Loop Formation ◽  
Surgical Interventions ◽  
Flexible Instrument

Abstract Flexible instruments are extensively used in medical applications. Manipulation of these instruments is challenging and troublesome. To study the behavior of these instruments, different modeling approaches like finite element, Cosserat rod, and differential geometry have been used. In this paper, an alternate modeling approach using Bézier curve is proposed to understand large deformation in a flexible instrument. The shape is represented by a Bézier curve. The deformation includes extension, flexure, and torsion in the instrument. Strain energy and geometric constraints are formulated using Bézier control points. The shape of the deformed instrument under the given constraints is obtained by minimizing the total strain energy. Nonlinear constrained optimization is used for minimization to find the deformed shape. The proposed method is applied for large elastic deformation in three-dimensional space. Loop formation is observed and validated with the experimental results. The proposed method will help in understanding the mechanics of a flexible instrument. Looping is a common problem during colonoscopy. The developed model will help in developing strategies for a safer introduction of these instruments inside the body for performing diagnostic and surgical interventions.

Modeling of Looping Behavior in a Flexible Instrument Using a Bélzier Curve

2021 ◽  
Author(s):  
Shobhit Singhal ◽  
Jitendra P. Khatait
Keyword(s):  
Strain Energy ◽  
Dimensional Space ◽  
Plane Deformation ◽  
Three Dimensional ◽  
Industrial Applications ◽  
Flexible Instrument ◽  
Out Of Plane ◽  
Minimum Strain Energy ◽  
And Control ◽  
Three Dimensional Space

Abstract Flexible medical instruments undergo looping during insertion and navigation inside the human body. It makes the control of the distal end difficult and raises safety concerns. This paper proposes the minimum strain energy concept to get the deformed shape of a flexible instrument in three-dimensional space. A B\'{e}zier curve is used to define the trajectory of the deformed shape under different loading conditions and constraints. Looping behavior is studied for different end shortening conditions. The effect of end twist on looping behavior is studied. It is observed that end twist leads to early onset of out of plane deformation leading to looping. The strain energy plot gives an insight into the behavior of these instruments with respect to end shortening and twist. The strain energy plot shows the minimum value for $2\pi$ end twist. Therefore, the instrument tends to go for looping if the end twist is present. Force and torque characteristics are obtained which will lead to the design and control of these instruments. Force and torque plots show negative stiffness when the instrument is going for looping. The un-looping phenomenon is also discussed and a strategy is proposed to mitigate looping. The proposed modeling approach can be utilized to address the complex behavior of a flexible instrument in medical as well as in other industrial applications. The insight developed will help in designing and developing control for safe and reliable usage of flexible instruments in various domains.

scholarly journals Interpolation method for quaternionic-Bezier curves

2018 ◽  
Vol 59 ◽  
pp. 13-18
Author(s):  
Severinas Zube
Keyword(s):  
Interpolation Method ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Three Dimensional Space ◽  
Tangent Vectors

We study rational quaternionic-Bézier curves in three dimensional space. We construct the quadratic quaternionic-Bézier curve which interpolates five points, or three points and two tangent vectors.

Initial design of low-thrust trajectories based on the Bezier curve-based shaping approach

2020 ◽  
Vol 234 (11) ◽  
pp. 1825-1835
Author(s):  
Zichen Fan ◽  
Mingying Huo ◽  
Naiming Qi ◽  
Ce Zhao ◽  
Ze Yu ◽  
...  
Keyword(s):  
Fourier Series ◽  
Three Dimensional ◽  
Initial Approximation ◽  
Mission Design ◽  
Bézier Curve ◽  
Design Stage ◽  
Bezier Curve ◽  
Series Method ◽  
Low Thrust ◽  
Fourier Series Method

This paper presents a method to use the Bezier curve to rapidly generate three-dimensional low-thrust trajectories, which can provide a suitable initial approximation to be used for more accurate trajectory optimal control tools. Two missions, from Earth to Mars and the asteroid Dionysus, are considered to evaluate the performance of the method. In order to verify the advantages of this method, it is compared with the finite Fourier series method. Numerical results show that the Bezier method can get better performance index in shorter computation time compared with the finite Fourier series method. The applicability of the solution obtained by Bezier method is evaluated by introducing the obtained solution into the Gauss pseudospectral method as an initial guess. The simulation results show that the Bezier method can rapidly generate a very suitable three-dimensional initial trajectory for the optimal solver. This is very important for rapid evaluation of the feasibility of a large number of low-thrust flight schemes in the preliminary mission design stage.

Cutaneous Receptive Field Organization in the Ventral Posterior Nucleus of the Thalamus in the Common Marmoset

1999 ◽  
Vol 82 (4) ◽  
pp. 1865-1875 ◽  
Author(s):  
P. Wilson ◽  
P. D. Kitchener ◽  
P. J. Snow
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Receptive Fields ◽  
Common Marmoset ◽  
The Body ◽  
Common Marmosets ◽  
Body Regions ◽  
Low Threshold ◽  
The Common ◽  
Receptive Field Organization

The organization of cutaneous receptive fields in the ventroposterior (VP) thalamus of the common marmosets ( Callithrix jacchus) was determined from single-unit recordings, and these data were correlated with the cytochrome oxidase (CO) histochemistry of the thalamus in the same animals. Under continuously maintained ketamine anesthesia, the receptive fields of a total of 192 single units were recorded from the right VP thalamus using 2 MΩ glass microelectrodes. After the receptive fields were mapped, the brains were reacted for CO histochemistry on 50-μm coronal frozen sections through the entire VP thalamus. The majority of units were localized to the CO-reactive regions that define the medial and lateral divisions of VP (VPm and VPl). Apart from the expected finding of the face being represented in VPm and the body in VPl, reconstructing the electrode tracks and unit locations in the histological sections revealed a general association between discrete regions of CO reactivity and the representation of specific body regions. Some low-threshold cutaneous units were apparently localized to VPi (the CO weak regions dorsal, ventral, and interdigitating with, the CO regions of VP). These VPi units were clearly part of the same representational map as the VPl and VPm units. We conclude that the low-threshold cutaneous receptive fields of the marmoset are organized in a single continuous representation of the contralateral body surface, and that this representation can most simply be interpreted as being folded or crumpled into the three-dimensional space of VP thalamus. The folded nature of the body map in VP may be related to the folded nature of VP as revealed by CO histochemistry.

Analysis on Structure and Morphological of Carton Packaging

2013 ◽  
Vol 442 ◽  
pp. 338-341
Author(s):  
A Qiang Sun
Keyword(s):  
Structural Design ◽  
Body Shape ◽  
Space Form ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Body ◽  
Packaging Materials ◽  
Paper Study ◽  
Structural Morphology ◽  
Three Dimensional Space

The package structure is a three-dimensional space form, so people know the products are in used in the packaging. In packaging materials for paper use is very extensive, paper products are easy to shape the body shape for easy printing and recyclable advantage. This paper study design of the paper packaging structural, combining paper packaging structural design applications to explore the paper packaging structural morphology and environmentalist design consciousness.

Elastic Fields in a Polyhedral Inclusion With Uniform Eigenstrains and Related Problems

2000 ◽  
Vol 68 (3) ◽  
pp. 441-452 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Stress Field ◽  
Strain Energy ◽  
Dimensional Space ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Elastic Field ◽  
Bounded Region ◽  
Symmetrical Structure ◽  
Elastic Fields ◽  
Three Dimensional Space

In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of three-dimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain energy for several major polyhedra and the effective stiffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eigenstrain do not coincide with those for a spherical inclusion (Eshelby’s solution) except for dodecahedron and icosahedron which belong to icosidodeca family, i.e., highly symmetrical structure.

Flight performance and visual control of flight of the free-flying housefly ( Musca domestica L.) I. Organization of the flight motor

1986 ◽  
Vol 312 (1158) ◽  
pp. 527-551 ◽  
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Midsagittal Plane ◽  
Torque Vector ◽  
Translation Velocity ◽  
Flight Motor

Free-flying houseflies have been filmed simultaneously from two sides. The orientation of the flies’ body axes in three-dimensional space can be seen on the films. A method is presented for the reconstruction of the flies’ movements in a fly-centred coordinate system, relative to an external coordinate system and relative to the airstream. The flies are regarded as three-dimensionally rigid bodies. They move with respect to the six degrees of freedom they thus possess. The analysis of the organization of the flight motor from the kinematic data leads to the following conclusions: the sideways movements can, at least qualitatively, be explained by taking into account the sideways forces resulting from rolling the body about the long axis and the influence of inertia. Thus, the force vector generated by the flight motor is most probably located in the fly’s midsagittal plane. The direction of this vector can be varied by the fly in a restricted range only. In contrast, the direction of the torque vector can be freely adjusted by the fly. No coupling between the motor force and the torques is indicated. Changes of flight direction may be explained by changes in the orientation of the body axes: straight flight at an angle of sideslip differing from zero is due to rolling. Sideways motion during the banked turns as well as the decrease of translation velocity observed in curves are a consequence of the inertial forces and rolling. The results are discussed with reference to studies about the aerodynamic performance of insects and the constraints for aerial pursuit.

scholarly journals Optimization of preoperative verification of isolated middle ear abnormalities using virtual ct endoscopy

2020 ◽  
Vol 19 (6) ◽  
pp. 16-22
Author(s):  
I. A. Anikin ◽  
◽  
S. V. Astashchenko ◽  
M. V. Komarov ◽  
S. N. Il’in ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Middle Ear ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Virtual Endoscopy ◽  
Ossicular Chain ◽  
Tympanic Cavity ◽  
Surgical Interventions ◽  
The Past ◽  
Virtual Ct

Isolated anomalies of the middle ear are one of the most difficult areas of practical otorhinolaryngology. Its relevance is due to the rare occurrence, high technical complexity of performing surgical treatment, and the high frequency of unsatisfactory results of surgical interventions. One of the most important factors determining the success of medical actions is high-quality X-ray imaging at the diagnostic stage. It allows you to correctly assess the anatomical features of the temporal bone and plan the tactics of the surgeon. Over the past few years, new technological possibilities have been introduced for the imaging of the ear. Over the past several decades, multispiral computed tomography has been the gold standard of radiation research used in otosurgery. This study has established itself as an informative method for diagnosing middle ear pathology and should be used before planning surgical interventions, as well as a monitoring tool in the postoperative period and for assessing the course of middle ear diseases. With the development of computer-mathematical technologies, over time, it became possible to model the result in three-dimensional space on the basis of axial projection, which led to the emergence of a branch of radiation diagnostics, called virtual CT endoscopy. The work evaluates the specificity of virtual CT endoscopy performed at the preoperative stage in patients with isolated anomalies of the ossicle chain with intact stapes, in terms of diagnosing the continuity of the ossicle chain, changes in their configuration and adhesions with the surrounding bone structures. A comparative analysis of the specificity of standard two-dimensional computed tomography and virtual CT endoscopy was performed, where explorative tympanotomy was used as test results in 43 patients. The advantages of virtual CT endoscopy in visualization of minor defects in the structures of the tympanic cavity were revealed. The importance of virtual CT endoscopy in measuring the tympanic cavity in arbitrary planes was determined. In addition to the above, virtual endoscopy opens up new possibilities for measuring the anatomical structures of the middle ear in arbitrary planes, which makes it possible, for example, to calculate the length of the prosthesis intended for use as plasty of the ossicular chain before surgery.

scholarly journals Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space

2021 ◽  
Vol 16 ◽  
pp. 73-84
Author(s):  
Maxim V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Fields ◽  
Characteristic Point ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Spatial Motion ◽  
Free Rigid Body

We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system

Directional Sensitivity of the Ears of Noctuid Moths

1966 ◽  
Vol 44 (1) ◽  
pp. 17-31
Author(s):  
R. S. PAYNE ◽  
K. D. ROEDER ◽  
J. WALLMAN
Keyword(s):  
Sound Source ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sound Intensity ◽  
Contralateral Side ◽  
The Body ◽  
Body Axis ◽  
Directional Sensitivity ◽  
Tympanic Organ ◽  
Three Dimensional Space

1. Noctuid moths of several species were mounted at the tip of a tower of fine tubing in acoustic ‘free space’. Recordings were made of the intensity of a brief pulse of ultrasound necessary to produce a constant tympanic nerve response for any angle of sound presentation relative to the moth's body axis. Such plots of intensity versus angle were made with the wings held in several postures approximating those assumed in normal flight. 2. The data indicate that sound intensity reaching the tympanic organ can vary by as much as 40 db. depending upon: (a) the position of a sound source relative to the moth's body axis, and (b) the position of its wings. 3. With wings above the horizontal plane each ear reports sounds c. 20-40 db. louder on the ipsilateral side than on the contralateral side. With wings below the horizontal, the lateral asymmetries are replaced by a dorsoventral asymmetry in which each ear reports sounds coming from below the body c. 10-25 db. louder than sounds coming from above. 4. Directional sensitivity plots at 60 kcyc./sec. are more complex than plots at 30 kcyc./sec.--as expected. 5. A theory is presented to explain how a moth could determine the direction of a sound source in three-dimensional space by comparing the intensity reports of both tympanic organs during a complete wing cycle.

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